If a population standard deviation is equal to 24.8, then the sampling distribution of the sample mean will have a standard deviation that is less than 24.8 for all possible sample sizes.

Question

If a population standard deviation is equal to 24.8, then the sampling distribution of the sample mean  will have a standard deviation that is less than 24.8 for all possible sample sizes.

Quizplus · Accepted Answer

This statement is true. The standard deviation of the sampling distribution of the sample mean decreases as the sample size increases, according to the formula SD(sample mean) = population SD / sqrt(sample size). Therefore, for all possible sample sizes, the standard deviation of the sampling distribution of the sample mean will be less than the population standard deviation of 24.8.

If a Population Standard Deviation Is Equal to 24